




"""simple docstring"""

a							      =     8.3_1_4_4_6_2  # Unit - J mol-1 K-1






def 		_snake_case	(   _snake_case				:   float							,    _snake_case				:   float							,    _snake_case				:   float				)       ->   float:






      '''simple docstring'''


      if moles < 0 or kelvin < 0 or volume < 0:
            raise ValueError('Invalid inputs. Enter positive value.'				)
      return moles * kelvin * UNIVERSAL_GAS_CONSTANT / volume






def 		_snake_case	(   _snake_case				:   float							,    _snake_case				:   float							,    _snake_case				:   float				)       ->   float:






      '''simple docstring'''


      if moles < 0 or kelvin < 0 or pressure < 0:
            raise ValueError('Invalid inputs. Enter positive value.'				)
      return moles * kelvin * UNIVERSAL_GAS_CONSTANT / pressure


if __name__ == "__main__":
       from doctest import testmod

       testmod()


"""simple docstring"""


def      lowerCamelCase_					(   __lowerCAmelCase							)				->   "list[int]":




						'''simple docstring'''



						if upper_limit < 0:
												raise ValueError("Limit for the Catalan sequence must be ≥ 0"							)

						lowerCamelCase__   =[0] * (upper_limit + 1)

						# Base case: C(0) = C(1) = 1
						lowerCamelCase__   =1
						if upper_limit > 0:
												lowerCamelCase__   =1

						# Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
						for i in range(2  ,       upper_limit + 1							):
												for j in range(__lowerCAmelCase							):
																		catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

						return catalan_list


if __name__ == "__main__":
	print('\n********* Catalan Numbers Using Dynamic Programming ************\n')
	print('\n*** Enter -1 at any time to quit ***')
	print('\nEnter the upper limit (≥ 0) for the Catalan number sequence: ', end='')
	try:
		while True:
			a				=int(input().strip())
			if N < 0:
				print('\n********* Goodbye!! ************')
				break
			else:
				print(F'''The Catalan numbers from 0 through {N} are:''')
				print(catalan_numbers(N))
				print('Try another upper limit for the sequence: ', end='')
	except (NameError, ValueError):
		print('\n********* Invalid input, goodbye! ************\n')

	import doctest

	doctest.testmod()


